What Happens When You Put Three Quantum Pigeons Into Two Pigeonholes?

You're all probably familiar with Schrodinger's Cat - the go-to quantum physics thought experiment. Well, now physicists have come up with a new animal metaphor to try and explain a complicated quantum principle.

The pigeonhole principle seems simple - if you put three pigeons in two pigeonholes, it is intuitive that at least two of the pigeons will end up in the same hole. But, as Yakir Aharonov and Jeff Tolaksen have discovered, this is not the case on the quantum level. They published a paper this month detailing their experiment, which demonstrated a violation of the pigeonhole principle with quantum particles and boxes. In the abstract, they explain, "We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box, a seemingly impossible and absurd effect."

But the laws governing the quantum world differ from those in the biological world. At the quantum level, things can be in multiple places at the same time - but only when not being observed. It's a similar principle to Schrodinger's Cat being "both alive and dead at the same time" until it is observed, which forces it to be either one or the other. Similarly, when the particles remain unobserved, they can be in two places at once, but when you observe a particle to see where it is, it acquires a specific position in one box or another.

Aharnov and his team have worked for two decades on new types of "weak measurements," which can see these linkages without actually "observing" them, "akin to tapping something softly with your finger rather than smashing it with that hammer, which forces each pigeon to be in a single box," explains Tolaksen.

Start with three particles and two boxes (we're not quite sure what "boxes" entails in this case, but we'll assume they're some sort of physical opening). Prepare the particles so that each one is in both of the two boxes at the same time - your basic quantum mechanical superposition of locations. You can now write the quantum equation for the state of all three particles, and use it to calculate the probabilities for what will happen when you actually look at the particles. Depending on how measurements are conducted, two particles are either in the same box, or not in the same box. So, you can have a situation where you have more particles than boxes, but no more than one particle in each box. At one point, the authors even point out that you can prepare the particles and conduct measurements in such a way that you get results dictating that Particle 2 is in the same box and Particle 1, and Particle 3 is in the same box as Particle 1, but Particles 2 and 3 are not in the same box.

"It is still very early to say that the full implications of this research are," said Tolaksen, "But we feel one should expect them to be major because we are dealing with such fundamental concepts."

"This discovery points to a very interesting structure of quantum mechanics that was hitherto unnoticed," added Aharonov, "This now requires us to revisit some of the most basic notions of nature."

Aharnov and Tolaksen think this new quantum conundrum can be of value in providing deeper insights into entanglement - the connection that links properties of each of a pair of particles, even when they are separated by a great distance. Even more significantly, this research could be a signal of further discoveries yet to come. As quantum mechanics nears its 90th birthday, physicists are still uncovering seemingly paradoxical, absurd, and groundbreaking principles that reshape the whole field, which means that there's still a long way to go before we truly understand what's happening on a quantum level.